Combine like terms. What is the simplest form of the expression?
`3(5-x)+4x(3x+2)`
*HINT: Don't forget that `x(x)=x^{2}`
To simplify the expression `3(5-x)+4x(3x+2)`, we can distribute the coefficients:
= `3*5-3*x+4*x*3*x+4*x*2`
= `15-3x+12x^2+8x`
Thus, the simplest form of the expression is `12x^2 + 5x + 15`.
To combine like terms and simplify the expression `3(5-x)+4x(3x+2)`, let's distribute first:
`= 3(5) - 3(x) + 4x(3x) + 4x(2)`
Now we simplify each term:
`= 15 - 3x + 12x^2 + 8x`
Next, let's rearrange the terms in ascending order of the exponent of `x`:
`= 12x^2 + 8x - 3x + 15`
Combining like terms:
`= 12x^2 + 5x + 15`
So, the simplest form of the expression `3(5-x) + 4x(3x+2)` is `12x^2 + 5x + 15`.
To combine like terms in the expression `3(5-x) + 4x(3x+2)`, we need to distribute and simplify each term.
Let's start by distributing `3` to `5-x`:
`3(5-x) = 3 * 5 - 3 * x = 15 - 3x`
Now, let's distribute `4x` to `3x+2`:
`4x(3x+2) = 4x * 3x + 4x * 2 = 12x^2 + 8x`
Now we can combine the simplified terms:
`15 - 3x + 12x^2 + 8x`
To combine like terms, we group the terms with the same variable and add their coefficients. In this case, we have `-3x` and `8x`, which have the same variable `x`. Thus, we can combine them as `-3x + 8x = 5x`.
Our final simplified expression is:
`12x^2 + 5x + 15`